A 'Professional Fit interview' is usually a non-technical interview by one or more people from the department you'd be hired into. It could be the senior manager who ultimately pays your salary, but it could also be a couple of engineers who are comfortable talking around various subjects to see if you'd fit in with a team like theirs.
There are some 'positive indicators' that they may be looking for (understands team work, can communicate, familiar with SDLC) that may not have been on your CV/resume nor come up in the technical interviews, but they're looking for them. Try to spot these and answer in a positive fashion. E.g.:
Question: What coding style do you use?
Good Answer: I'll take cues from the style of surrounding lines of code to ensure consistency, or ask colleagues about the team style.
Bad Answer: I like to re-format all code I work on to fit my personal tab/brace/naming style. It's so much better than anything else (yes, I've heard this)
There are some items that would count as 'negative indicators'. It may be illegal/bad form to ask certain questions in an interview (e.g. in UK can't ask about family, marital status, gender or religion), so they may want to talk around the subject until you accidentally let slip something they feel may be a problem for them.
Yes, this is immoral, but it happens in real life. I have seen people rejected because they were gender-unsure even though they were brilliant programmers. I have also seen excellent engineers hired by HR departments but then get ostracised by the team as they just didn't get along with anyone in the team.
Don't volunteer anything you don't need to. For example, no need to mention that you're thinking of starting a family next year - it's none of their business, but some interviewers would immediately think "has outside commitments to distract him from the job". If you can get to the office by ~9am and do a full days' work, no need to make them think that you can't.
My top tips for getting through this:
- Dress smart. You need to look 'professional', even if the dress code is metal T-shirt and ripped jeans.
- Professional, objective responses. Don't run your mouth off over anything - you may be lulled into doing so (a common technique), but try to stay on-topic.
- Do some homework before the interview. Try to have a better understanding of their company, their projects/goals, the market they operate in, etc. As this is interview is further through the process, you should be demonstrably more interested in the job.
- Be straight with them. Tell the truth. If you don't know, just say - don't waste anyone's time. If you're caught bending the truth, you'd likely fail your probationary period or (worse) be sued.
- Be alert - although the person interviewing you may seem detached from the job you've applied for, they may try to throw in the occasional technical question to make their own assessment of you or to see you how react. I once had a CTO-level guy in a finance company ask me to compare and contrast two embedded O/S's approach to device drivers. Yep, really.